Rodrigues was born into a well-to-do Sephardi Jewish family in Bordeaux.

During this period, Rodrigues published writings on politics, social reform, and banking.

[9] It uses three numbers to parameterize the entries of a rotation matrix using only rational functions.

When converted to four parameters, this representation is equivalent to a unit-norm quaternion, and describes the axis and angle of a rotation.

[10][11] In 1846, Arthur Cayley acknowledged[12] Euler's and Rodrigues' priority describing orthogonal transformations.